Lesson Title: Distributed Mass and Restoring Force
State Standards: GLEs/GSEs
National Standards:
Context of Lesson:
The previous lesson introduced Harmonic Motion with discrete systems:
Pendulum Motion, Water in U-Tube, Mass on a Spring.
This lesson continues the concept of a Restoring Force and Harmonic Motion to more "real world" examples:
Vibrating String, Chimes, Drums, and Air Columns, all familiar as the basis of musical instruments.
The same remarks apply to the other systems, but they are not as easy to see.
Strings
Chimes
Air Columns
Drums
Opportunities to Learn:
As in the previous lesson, students first opportunity to learn is by hands-on experiment,
and the second is by analysis of what was observed.
Because in these systems, the mass and restoring force are properties of some continuous material, rather than separate components, the required analysis is more subtle. Methods typically used are to assume an "arbitrarily small part" of a continuous
material, assume that for "small" angles, the sin function, or most other functions, may be approximated by a linear slope, and other tricks that seem to violate common sense, yet can be justified. This may be the student's first introduction to these techniques, and that is the third opportunity to learn.
Depth of Knowledge
Dok1 and Dok2
This lesson extends the concept of Harmonic Motion to systems in which the mass and restoring force are properties of some continuous material, rather than separate components, and gives students hands-on examples to work with,
and observe while varying certain parameters.
Students are asked to note which parameters caused changes in system behavior,
and to note the similarities and differences of the different example systems.
This is followed by a lecture in which the mechanical systems are analyzed,
and the observations compared to the analysis.
Prerequisite Knowledge
Students have learned about systems with a discrete mass and restoring force, and how those systems support Harmonic motion.
Rhode Island Department of Education Lesson Plan
Lesson Title: Distributed Mass and Restoring Force
State Standards: GLEs/GSEs
National Standards:
Context of Lesson:
The previous lesson introduced Harmonic Motion with discrete systems:
Pendulum Motion, Water in U-Tube, Mass on a Spring.
This lesson continues the concept of a Restoring Force and Harmonic Motion to more "real world" examples:
Vibrating String, Chimes, Drums, and Air Columns, all familiar as the basis of musical instruments.
The same remarks apply to the other systems, but they are not as easy to see.
Opportunities to Learn:
As in the previous lesson, students first opportunity to learn is by hands-on experiment,
and the second is by analysis of what was observed.
Because in these systems, the mass and restoring force are properties of some continuous material, rather than separate components, the required analysis is more subtle. Methods typically used are to assume an "arbitrarily small part" of a continuous
material, assume that for "small" angles, the sin function, or most other functions, may be approximated by a linear slope, and other tricks that seem to violate common sense, yet can be justified. This may be the student's first introduction to these techniques, and that is the third opportunity to learn.
Depth of Knowledge
Dok1 and Dok2
This lesson extends the concept of Harmonic Motion to systems in which the mass and restoring force are properties of some continuous material, rather than separate components, and gives students hands-on examples to work with,
and observe while varying certain parameters.
Students are asked to note which parameters caused changes in system behavior,
and to note the similarities and differences of the different example systems.
This is followed by a lecture in which the mechanical systems are analyzed,
and the observations compared to the analysis.
Prerequisite Knowledge
Students have learned about systems with a discrete mass and restoring force, and how those systems support Harmonic motion.
Plans for Differentiating Instruction
As in previous lesson.
Accommodations and modifications
Environmental factors
Materials
Objectives:
Instruction:
Opening:
Engagement:
Closure:
Assessment:
Reflections
(only done after lesson is enacted)Student Work Sample 1 – Approaching Proficiency:
Student Work Sample 2 – Proficient:
Student Work Sample 3 – Exceeds Proficiency: